Fluid-Electro-Mechanical Parametric Model of the Left Ventricle (original) (raw)
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Mathematical Modeling the Electrical Activity of the Heart
Proceedings of the 2016 Conference on Information Technologies in Science, Management, Social Sphere and Medicine
Nowadays, due to the prevalence of cardiovascular diseases there is extremely high demand not only in the development of new means of treatment and diagnosis, but also in their wider implementation in practice. Improving the efficiency of non-invasive diagnostic techniques, in our opinion, is one of the key tasks, the solution of which will significantly help in the treatment of cardiovascular diseases. The achievements of modern science, in particular-biology, biophysics and cybernetics, provide great opportunities to solve this problem through the development of mathematical models of cardiac electrical activity. The purpose of this article is to review the heart electrophysiology and the main approaches to the modeling of cardiac electrical activity as well as specific models.
arXiv (Cornell University), 2020
We propose an integrated electromechanical model of the human heart, with focus on the left ventricle, wherein biophysically detailed models describe the different physical phenomena concurring to the cardiac function. We model the subcellular generation of active force by means of an Artificial Neural Network, which is trained by a suitable Machine Learning algorithm from a collection of pre-computed numerical simulations of a biophysically detailed, yet computational demanding, high-fidelity model. To provide physiologically meaningful results, we couple the 3D electromechanical model with a closed-loop 0D (lumped parameters) model describing the blood circulation in the whole cardiovascular network. We prove that the 3D-0D coupling of the two models is compliant with the principle of energy conservation, which is achieved in virtue of energy-consistent boundary conditions that account for the interaction among cardiac chambers within the computational domain, pericardium and surrounding tissue. We thus derive an overall balance of mechanical energy for the 3D-0D model. This provides a quantitative insight into the energy utilization, dissipation and transfer among the different compartments of the cardiovascular network and during different stages of the heartbeat. In virtue of this new model and the energy balance, we propose a new validation tool of heart energy usage against relationships used in the daily clinical practice. Finally, we provide a mathematical formulation of an inverse problem aimed at recovering the reference configuration of one or multiple cardiac chambers, starting from the stressed configuration acquired from medical imaging. This is fundamental to correctly initialize electromechanical simulations. Numerical methods and simulations of the 3D-0D model will be detailed in Part II.
Mathematical Modelling of Human Heart as a Hydroelectromechanical System
Different electrical models of human heart, partial or complete, with linear or nonlinear models have been developed. In the literature, there are some applications of mathematical and physical analog models of total artificial heart (TAH), a baroreceptor model, a state-space model, an electromechanical biventricular model of the heart, and a mathematical model for the artificial generation of electrocardiogram (ECG) signals. Physical models are suitable to simulate real physiological data based on proper experimental set up present. This paper introduces a new mathematical modelling of human heart as a hydroelectromechanical system (HEMS). This paper simulates the human heart based on three main functions: hydraulic, electrical and mechanical parameters. Hydro-mechanical model developed then has been transformed into electrical domain and simulation has been carried out according to the mathematical model or formulations obtained using Laplace transform. This electrical model / circuit is then tested by MATLAB based simulations and results found are comparable with the normal ECG waveforms so that these simulated results may be useful in clinical experiments. In this model basic electrical components have been used to simulate the physiological functions of the human heart. The result is a simple electrical circuit consisting of main electrical parameters that are transformed from hydraulic models and medical physiological values. Developed MATLAB based mathematical model will primarely help to understand the proper functioning of an artificial heart and its simulated ECG signals. A comprehensive model for generating a wide variety of such signals has been targeted for future in this paper. This research especially focuses on modelling human heart as a hydro-electro-mechanical system with three case studies.
A new hybrid electro-numerical model of the left ventricle
Computers in Biology and Medicine, 2008
The paper presents a new project of a hybrid numerical-physical model of the left ventricle. A physical part of the model can be based on electrical or hydraulic structures. Four variants of the model with numerical and physical heart valves have been designed to investigate an effect of a heart assistance connected in series and in parallel to the natural heart. The LabVIEW TM real time environment has been used in the model to increase its accuracy and reliability. A prototype of the hybrid electro-numerical model of the left ventricle has been tested in an open loop and closed loop configuration.
An electromechanics-driven fluid dynamics model for the simulation of the whole human heart
arXiv (Cornell University), 2023
We introduce a multiphysics and geometric multiscale computational model, suitable to describe the hemodynamics of the whole human heart, driven by a four-chamber electromechanical model. We first present a study on the calibration of the biophysically detailed RDQ20 activation model (Regazzoni et al., 2020) that is able to reproduce the physiological range of hemodynamic biomarkers. Then, we demonstrate that the ability of the force generation model to reproduce certain microscale mechanisms, such as the dependence of force on fiber shortening velocity, is crucial to capture the overall physiological mechanical and fluid dynamics macroscale behavior. This motivates the need for using multiscale models with high biophysical fidelity, even when the outputs of interest are relative to the macroscale. We show that the use of a high-fidelity electromechanical model, combined with a detailed calibration process, allows us to achieve a remarkable biophysical fidelity in terms of both mechanical and hemodynamic quantities. Indeed, our electromechanical-driven CFD simulationscarried out on an anatomically accurate geometry of the whole heart-provide results that match the cardiac physiology both qualitatively (in terms of flow patterns) and quantitatively (when comparing in silico results with biomarkers acquired in vivo). Moreover, we consider the pathological case of left bundle branch block, and we investigate the consequences that an electrical abnormality has on cardiac hemodynamics thanks to our multiphysics integrated model. The computational model that we propose can faithfully predict a delay and an increasing wall shear stress in the left ventricle in the pathological condition. The interaction of different physical processes in an integrated framework allows us to faithfully describe and model this pathology, by capturing and reproducing the intrinsic multiphysics nature of the human heart.
Mathematical and numerical models for the cardiac electromechanical function
Rendiconti Lincei - Matematica e Applicazioni, 2021
This paper deals with the mathematical model that describes the function of the human heart. More specifically, it addresses the equations that express the electromechanical process, that is the mechanical deformation (contraction and relaxation) of the heart muscle that is induced by the electrical field that, at every heartbeat, is generated in the sino-atrial node and then propagates all across the cardiac cells. After deriving the equations of the mathematical model from basic physical principles, we proceed to their numerical approximations and discuss issues such as stability, accuracy and computational complexity. We close the paper by illustrating a few numerical results on test problems of potential interest for clinical applications.
Modeling the cardiac electromechanical function: A mathematical journey
Bulletin of the American Mathematical Society
In this paper we introduce the electromechanical mathematical model of the human heart. After deriving it from physical first principles, we discuss its mathematical properties and the way numerical methods can be set up to obtain numerical approximations of the (otherwise unachievable) mathematical solutions. The major challenges that we need to face—e.g., possible lack of initial and boundary data, the trade off between increasing the accuracy of the numerical model and its computational complexity—are addressed. Numerical tests here presented have a twofold aim: to show that numerical solutions match the expected theoretical rate of convergence, and that our model can provide a preliminary valuable tool to face problems of clinical relevance.